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Proc Natl Acad Sci U S A. 2008 Dec 9;105(49):19235-40. doi: 10.1073/pnas.0805344105. Epub 2008 Nov 25.

Ordered cyclic motifs contribute to dynamic stability in biological and engineered networks.

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Department of Pharmacology and Systems Therapeutics, Mount Sinai School of Medicine, 1 Gustave Levy Place, New York, NY 10029, USA.


Representation and analysis of complex biological and engineered systems as directed networks is useful for understanding their global structure/function organization. Enrichment of network motifs, which are over-represented subgraphs in real networks, can be used for topological analysis. Because counting network motifs is computationally expensive, only characterization of 3- to 5-node motifs has been previously reported. In this study we used a supercomputer to analyze cyclic motifs made of 3-20 nodes for 6 biological and 3 technological networks. Using tools from statistical physics, we developed a theoretical framework for characterizing the ensemble of cyclic motifs in real networks. We have identified a generic property of real complex networks, antiferromagnetic organization, which is characterized by minimal directional coherence of edges along cyclic subgraphs, such that consecutive links tend to have opposing direction. As a consequence, we find that the lack of directional coherence in cyclic motifs leads to depletion in feedback loops, where the number of nodes affected by feedback loops appears to be at a local minimum compared with surrogate shuffled networks. This topology provides more dynamic stability in large networks.

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